Finite-time generalization of the thermodynamic uncertainty relation

Understand

For fluctuating currents in non-equilibrium steady states, the recently discovered thermodynamic uncertainty relation expresses a fundamental relation between their variance and the overall entropic cost associated with the driving.

• We show that this relation holds not only for the long-time limit of fluctuations, as described by large deviation theory, but also for fluctuations on arbitrary finite time scales.
• This generalization facilitates applying the thermodynamic uncertainty relation to single molecule experiments, for which infinite timescales are not accessible.
• Importantly, often this finite-time variant of the relation allows inferring a bound on the entropy production that is even stronger than the one obtained from the long-time limit.